In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism (HS) with indicative conditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicative conditionals.

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

Boethius' treatise De Hypotheticis Syllogismis provided twelfth-century philosophers with an introduction to the logic of conditional and disjunctive sentences but this work is the only part of the logica vetus which is no longer studied in the twelfth century. In this paper I investigate why interest in Boethius acount of hypothetical syllogisms fell off so quickly. I argue that Boethius' account of compound sentences is not an account of propositions and once a proper notion of propositionality is available the argument (...) forms accepted by Boethius are seen to be incoherent. It was Peter Abaelard who first understood the nature of propositionality and propositional connectives and used this to criticise Boethius' claims in De Hypothetics Syllogismis. In place Boethius' confusion Abaelard offered a simple and correct account of the hypothetical syllogism. (shrink)

Comparative syllogism is a type of scientific reasoning widely used, explicitly or implicitly, for inferences from observations to conclusions about effectiveness, but its philosophical significance has not been fully elaborated or appreciated. In its simplest form, the comparative syllogism derives a conclusion about the effectiveness of a factor (e.g. a treatment or an exposure) on a certain property via an experiment design using a test (experimental) group and a comparison (control) group. Our objective is to show that the (...) comparative syllogism can be understood as encoding a simulation view of counterfactuals, in that counterfactual situations are conceptual constructs that can be correctly simulated by homogeneous comparison groups. In this simulation view, the empirical data from the comparison groups play an evidential role in the evaluation of counterfactuals and in obtaining counterfactual knowledge. We further indicate how successful experimental designs can help us to obtain correct simulations, and thus to bring us to scientifically-empirically based counterfactual knowledge. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical (...)Syllogism. The improved proof relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

The hypothetical syllogism is invalid in standard interpretations of conditional sentences. Many arguments of this sort are quite compelling, though, and you can wonder what makes them so. I shall argue that it is our parsimony in regard to connections among events and states of affairs. All manner of things just might, for all we know, be bound up with one another in all sorts of ways. But ordinarily it is better, being simpler, to assume they are unconnected. In (...) so doing, we jump to the conclusions of some compelling but invalid arguments. (shrink)

This article tackles a number of puzzles related to Aristotle’s practical syllogism, notably the relationship between deliberation and the practical syllogism, the distinction between deliberative and reconstructive practical syllogisms, and the nature of the conclusion of the practical syllogism.

Following H. T. Colebrooke's 1824 'discovery' of the Hindu syllogism, his term for the five-step inference schema in the "Nyāya-sūtra," European logicians and historians of philosophy demonstrated considerable interest in Indian logical thought. This is in marked contrast with later historians of philosophy, and also with Indian nationalist and neo-Hindu thinkers like Vivekananda and Radhakrishnan, who downgraded Indian rationalist traditions in favor of 'spiritualist' or 'speculative' texts. This article traces the role of these later thinkers in the origins of (...) the myth that Indian thought is spiritual and arational. The extent to which nineteenth-century European philosophers were aware of Colebrooke's 'discovery' is documented, and then their criticisms of the Hindu syllogism and its defense by orientalists like Ballantyne and Müller are examined. (shrink)

It is well-known that the Arab philosophers of the Aristotelian tradition, like some of their Alexandrian predecessors, attached rhetoric and poetics to logic, and supported this inclusion by the idea that the principal poetic procedure - that is, essentially, metaphor - is a kind of syllogism: the poetic syllogism. However, until now, no texts prior to those of Avicenna had been identified which render the structure of this syllogism explicit. In the present contribution, we present and translate (...) a passage from al-Farabi which shows that for him, the poetic syllogism is an incorrect syllogism of the second figure - a different interpretation from that which will be given by Avicenna. (shrink)

Disjunctive Syllogism, that is, the inference from 'not-A or B' and 'A', to 'B' can lead from true premises to a false conclusion if each of the sentences 'A' and 'not-A' is a statement of a partial truth such that affirming one of them amounts to denying the other, without each being the contradictory of the other. Such sentences inevitably occur whenever a situation which for its proper precise description needs the use of expressions such as 'most probably true' (...) and so forth, is described (less precisely) by sentences not containing such expressions. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

We provide Routley-Meyer type semantics for relevant logics including Contractionless Ticket Entailment TW (without the truth constant t and o) plus reductio R and Ackermann’s rule γ (i.e., disjunctive syllogism). These logics have the following properties. (i) All have the variable sharing property; some of them have, in addition, the Ackermann Property. (ii) They are stable. (iii) Inconsistent theories built upon these logics are not necessarily trivial.

While accepting that distribution is a coherent notion, I argue that it is nevertheless irrelevant to the working of the syllogism. Instead, I propose: (i) that a term's being distributed or undistributed in a proposition is its capacity to be replaced in a truth-preserving substitution with a narrower or a wider term; (ii) that which capacity the term has is determined by whether it occurs as the predicate of a negative or of an affirmative statement of the proposition; and (...) (iii) that it is only the term's occurrence as the predicate of a negative or an affirmative statement–rather than its distribution value–that is relevant to syllogistic entailment. (shrink)

The thesis here expounded can be divided in three parts: in the first place, it is supposed that the syllogism is not the rhetorical way, and less still the logical way, indeed used to reach the decision in the legal proceedings monopolized by the modern State. At the most, it can be seen as a form of presenting a decision that has already been reached by other means. It sure constitutes a highly functional procedure, effective and legitimating. It is (...) generally not a conscious strategy on the part of the so called official legal agents (judges, prosecutors, state attorneys, lawyers, plaintiffs), which seem to believe that the decision before the concrete case is in fact produced by the previous general norm enunciated by the system. If there would be a chronological order, the general norm comes afterwards. In the second place, the judicial discursive structure seems to be rather enthymematic than syllogistic, because not all the effectively used norms are revealed, many of them staying not only out of question but also hidden. Finally, it is suggested that, in the atmosphere of faking dogmatic law in which acts the underdeveloped State, those implicit norms are not just presupposed as evident, but they are also uncertain, being rendered to manipulation. (shrink)

This article contains the proof of equivalence boolean algebra and syllogistics arc2. The system arc2 is obtained as a superstructure above the propositional calculus. Subjects and predicates of syllogistic functors a, E, J, O may be complex terms, Which are formed using operations of intersection, Union and complement. In contrast to negative sentences the interpretation of affirmative sentences suggests non-Empty terms. To prove the corresponding theorem we demonstrate that boolean algebra is included into syllogistics arc2 and vice versa.

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantiﬁcation. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

This paper introduces the reader to the medieval Hebrew tradition of logic by considering its treatment of Aristotelian syllogistic. Starting in the thirteenth century European Jews translated Arabic and Latin texts into Hebrew and produced commentaries and original compendia.Because they stood culturally and geographically at the cross-roads of two great traditions they were influenced by both.This is clearly seen in the development of syllogistic theory, where the Latin tradition ultimately replaces, though never entirely, its Arabic counterpart.Specific attention is devoted to (...) the debate about the so-called Galenian fourth figure.In medieval Hebrew logic one finds both defenders and detractors of the figure, the former appearing towards the beginning of the period in question.With the ascendancy of scholastic logic the fourth figure virtually disappears from Hebrew texts. (shrink)

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.

This article discusses how inference to the best explanation (IBE) can be justified as a practical meta-argument. It is, firstly, justified as a practical argument insofar as accepting the best explanation as true can be shown to further a specific aim. And because this aim is a discursive one which proponents can rationally pursue in—and relative to—a complex controversy, namely maximising the robustness of one’s position, IBE can be conceived, secondly, as a meta-argument. My analysis thus bears a certain analogy (...) to Sellars’ well-known justification of inductive reasoning (Sellars, In: Essays in honour of Carl G. Hempel, 1969); it is based on recently developed theories of complex argumentation (Betz, In: Theorie dialektischer Strukturen, 2010a). (shrink)

Avicenna refers on a number of occasions in his Book of the Syllogism to “the eminent later scholar” . At least three recent studies have argued or assumed that this eminent later scholar is Alexander of Aphrodisias. It is argued in this article that Avicenna is in fact referring to Alfarabi. This has consequences for reconstructing the lost first part of Alfarabi's Great Commentary on the Prior Analytics , for highlighting certain aspects of Alfarabi's logical doctrines, and for understanding (...) more about the relation between Avicenna and Alfarabi in matters logical. (shrink)